Are the following statement forms logically equivalent p V q

Are the following statement forms logically equivalent? p V q rightarrow p and p (- p q)? Include a truth table and a few words explaining how the e supports your answer. Write the converse, inverse, and contrapositive of \"If Ann is Jan\'s mother, then Jose is Jan\'s cousin.\" Write the converse, inverse, and contrapositive of \"If Ed is Sue\'s father, then Liu is Sue\'s cousin.\" Write the converse, inverse, and contrapositive of \"If Al is Tom\'s cousin, then Jim is Tom\'s grandfather.\"

Solution

From the above table, (4) and (7) are not the same. Therefore, the given statements are logically not the same.

6. If Ann is Jan\'s mother, then Jose is Jan\'s cousin.

Converse: If Jose is Jan\'s cousin, then Ann is Jan\'s mother.

Inverse: If Ann is not Jan\'s mother, then Jose is not Jan\'s cousin.

Contrapositive: If Jose is not Jan\'s cousin, then Ann is not Jan\'s mother.

7. If Ed is Sue\'s father, then Liu is Sue\'s cousin.

Converse: If Liu is Sue\'s cousin, then Ed is Sue\'s father.

Inverse: If Ed is not Sue\'s father, then Liu is not Sue\'s cousin.

Contrapositive: If Liu is not Sue\'s cousin, then Ed is not Sue\'s father.

8. If Al is Tom\'s cousin, then Jim is Tom\'s grandfather.

Converse: If Jim is Tom\'s grandfather, then Al is Tom\'s cousin.

Inverse: If Al is not Tom\'s cousin, then Jim is not Tom\'s grandfather.

Contrapositive: If Jim is not Tom\'s grandfather, then Al is not Tom\'s cousin.

P(1)	Q(2)	P V Q(3)	(3) -> P (4)	~P(5)	~P ^ Q(6)	P V (6) (7)
0	0	0	1	1	0	0
0	1	1	0	1	1	1
1	0	1	1	0	0	1
1	1	1	1	0	0	1